| In this thesis, the problem of regularized image restoration without any prior information about the original image and noise is considered. A new paradigm is adopted, according to which the required prior information is extracted from the available data at the previous iteration step, i.e., the partially restored image at each step. This new paradigm is based on the fact that the restored image or available data at a certain iteration step include information about the original image and the noise. In order for this approach to be meaningful, the iteration steps should be within a certain allowable range, in other words, the iteration should be guaranteed to converge to a reasonable solution.; The main issues which are addressed in this thesis are: (a) how to control the solution procedure to guarantee a desirable solution and (b) how to estimate the information about the original image and the noise process required for regularization at every iteration step.; A general form of a weighted smoothing functional is proposed. The form of the functional is motivated in two ways: by considering the correspondence between deterministic regularization and Bayesian or stochastic regularization and also for incorporating spatial adaptivity into the restoration process. The proposed new smoothing functional is defined to have a unique minimizer, therefore, the solution procedure is guaranteed to converge to a desirable globally optimal solution. The proposed generalized iteration adaptive regularization approach is extended to a multichannel algorithm, which is based on the minimum multichannel regularized noise power criterion and the incorporation of the auto and cross channel information into the algorithm. The proposed multichannel algorithm is shown to be much more computationally efficient than existing algorithms, and furthermore, it is not dependent upon the initial conditions.; Finally, in this thesis the possibility of using the new regularization approaches, in other applications, such as, astronomical data processing, edge enhancement and deterministic estimation of higher order spectra, is demonstrated. |
